{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T12:54:31Z","timestamp":1777640071439,"version":"3.51.4"},"reference-count":6,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper considers three approaches to choosing the constant <jats:italic>H<\/jats:italic> in the expression <jats:inline-formula id=\"j_mcma-2024-2004_ineq_9999\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mrow>\n                                 <m:mi>H<\/m:mi>\n                                 <m:mo>\u2062<\/m:mo>\n                                 <m:msqrt>\n                                    <m:mrow>\n                                       <m:mi>\ud835\udc03<\/m:mi>\n                                       <m:mo>\u2062<\/m:mo>\n                                       <m:mi>\u03b6<\/m:mi>\n                                    <\/m:mrow>\n                                 <\/m:msqrt>\n                              <\/m:mrow>\n                              <m:mo>\/<\/m:mo>\n                              <m:msqrt>\n                                 <m:mi>n<\/m:mi>\n                              <\/m:msqrt>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_mcma-2024-2004_eq_0044.png\"\/>\n                        <jats:tex-math>{H\\sqrt{{\\mathbf{D}}\\zeta}\/\\sqrt{n}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> for the error of the Monte Carlo method for numerical calculation of mathematical expectation <jats:inline-formula id=\"j_mcma-2024-2004_ineq_9998\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi>\ud835\udc04<\/m:mi>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:mi>\u03b6<\/m:mi>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_mcma-2024-2004_eq_0114.png\"\/>\n                        <jats:tex-math>{{\\mathbf{E}}\\zeta}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> of a random variable \u03b6: in probability, in mean square and in mean.In practical studies using the Monte Carlo method, when estimating the calculation error, it is recommended to use the \u201cin mean\u201d approach with the constant <jats:inline-formula id=\"j_mcma-2024-2004_ineq_9997\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi>H<\/m:mi>\n                              <m:mo>=<\/m:mo>\n                              <m:msqrt>\n                                 <m:mfrac>\n                                    <m:mn>2<\/m:mn>\n                                    <m:mi>\u03c0<\/m:mi>\n                                 <\/m:mfrac>\n                              <\/m:msqrt>\n                              <m:mo>=<\/m:mo>\n                              <m:mrow>\n                                 <m:mn>0.79788456079<\/m:mn>\n                                 <m:mo>\u2062<\/m:mo>\n                                 <m:mi mathvariant=\"normal\">\u2026<\/m:mi>\n                              <\/m:mrow>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_mcma-2024-2004_eq_0043.png\"\/>\n                        <jats:tex-math>{H=\\sqrt{\\frac{2}{\\pi}}=0.79788456079\\dots}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>\u2009\u2009.<\/jats:p>","DOI":"10.1515\/mcma-2024-2004","type":"journal-article","created":{"date-parts":[[2024,4,23]],"date-time":"2024-04-23T18:26:53Z","timestamp":1713896813000},"page":"131-136","source":"Crossref","is-referenced-by-count":3,"title":["Choice of a constant in the expression for the error of the Monte Carlo method"],"prefix":"10.1515","volume":"30","author":[{"given":"Viktor","family":"Bryzgalov","sequence":"first","affiliation":[{"name":"Lyceum No. 130 , Novosibirsk , Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nurlibay","family":"Shlimbetov","sequence":"additional","affiliation":[{"name":"Novosibirsk State University , Novosibirsk , Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anton","family":"Voytishek","sequence":"additional","affiliation":[{"name":"Institute of Computational Mathematics and Mathematical Geophysics , Russian Academy of Sciences , Novosibirsk State University , Novosibirsk , Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2024,4,24]]},"reference":[{"key":"2024052809495391089_j_mcma-2024-2004_ref_001","unstructured":"A. V.  Voytishek,\nLectures on Monte Carlo Methods (in Russian),\nIPC NSU, Novosibirsk, 2018."},{"key":"2024052809495391089_j_mcma-2024-2004_ref_002","unstructured":"A. A.  Borovkov,\nProbability Theory (in Russian),\nNauka, Moscow, 1976."},{"key":"2024052809495391089_j_mcma-2024-2004_ref_003","unstructured":"A. A.  Borovkov,\nMathematical Statistics (in Russian),\nNauka, Moscow, 1984."},{"key":"2024052809495391089_j_mcma-2024-2004_ref_004","unstructured":"V. L.  Bryzgalov and A. V.  Voytishek,\nEstimation of the constant in the expression for the error of the Monte Carlo method (in Russian),\nInformation Technologies and Mathematical Modelling (ITMM\u20132022),\nTomsk State University, Tomsk (2023), 265\u2013270."},{"key":"2024052809495391089_j_mcma-2024-2004_ref_005","unstructured":"I. M.  Sobol,\nNumerical Monte Carlo Methods (in Russian),\nNauka, Moscow, 1973."},{"key":"2024052809495391089_j_mcma-2024-2004_ref_006","unstructured":"A. V.  Voytishek and E. N.  Andornii,\nOn the choice of a constant in the expression for the error of the Monte Carlo method (in Russian),\nAbstracts of the International Conference \u201cAdvanced Problems of Computational and Applied Mathematics \u2013 2015\u201d,\nAkademizdat, Novosibirsk (2015), 1\u201332."}],"container-title":["Monte Carlo Methods and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2024-2004\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2024-2004\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,28]],"date-time":"2024-05-28T09:50:40Z","timestamp":1716889840000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2024-2004\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,24]]},"references-count":6,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,10,24]]},"published-print":{"date-parts":[[2024,6,1]]}},"alternative-id":["10.1515\/mcma-2024-2004"],"URL":"https:\/\/doi.org\/10.1515\/mcma-2024-2004","relation":{},"ISSN":["0929-9629","1569-3961"],"issn-type":[{"value":"0929-9629","type":"print"},{"value":"1569-3961","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,24]]}}}